Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 045, 21 pages      arXiv:0712.1718
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy

George Yu. Bogoslovsky
Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Moscow, Russia

Received December 09, 2007, in final form May 08, 2008; Published online May 26, 2008

We study the geometric phase transitions that accompany the dynamic rearrangement of vacuum under spontaneous violation of initial gauge symmetry. The rearrangement may give rise to condensates of three types, namely the scalar, axially symmetric, and entirely anisotropic condensates. The flat space-time keeps being the Minkowski space in the only case of scalar condensate. The anisotropic condensate having arisen, the respective anisotropy occurs also in space-time. In this case the space-time filled with axially symmetric condensate proves to be a flat relativistically invariant Finslerian space with partially broken 3D isotropy, while the space-time filled with entirely anisotropic condensate proves to be a flat relativistically invariant Finslerian space with entirely broken 3D isotropy. The two Finslerian space types are described briefly in the extended introduction to the work, while the original part of the latter is devoted to determining observable 3-velocities in the entirely anisotropic Finslerian event space. The main difficulties that are overcome in solving that problem arose from the nonstandard form of the light cone equation and from the necessity of correct introducing of a norm in the linear vector space of rapidities.

Key words: Lorentz, Poincaré, and gauge invariances; spontaneous symmetry breaking; dynamic rearrangement of vacuum; Finslerian space-time.

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